The beam in the figure below $(L=4m$ and $EI=2000kN{m}^2)$ is fixed at both ends. Use FDM with $h=1m$ to:

A$)$ Formulate five equations using the governing ODE, $q(x)=EI\frac{d^{4}y(x)}{d{x}^4}.$

$(1$ mark$)$

B$)$ Use boundary conditions to reduce the nine unknowns in a$)$ to five.

$(1$ mark$)$

C$)$ Use symmetry to reduce the five equations to three.

D$)$ Use the equations in iv$)$ to solve for the unknowns.

$(1$ mark$)$

E$)$ Determine the bending moment at $x=0.$

$(1$ mark$)$

Note: The $30kN$ force is at the center of the beam

$(1$ mark$)$

Pls solve step by step with all details